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safe to use endogenous variables as instruments is at least one 
less for use in higher-numbered than for use in the same or 
lower-numbered sectors. 
As a matter of fact, our result is a bit stronger than this. 
It is apparent from (5.26) that the use of endogenous variables 
lagged 0% periods as instruments in higher-numbered sectors 
involves covariances of the order of A+!H. Even the use of 
endogenous variables lagged 6*+1 periods as instruments in 
the same or lower-numbered sectors, however, involves cova- 
riances of the order of only A® +1. No positive power of H is 
involved in the first term of the expansion for the latter co- 
variances. Since H is diagonal with diagonal elements less 
than unity in absolute value, the difference between the mini- 
mum lag with which it is safe to use endogenous variables as 
instruments in the same or lower-numbered sectors and the 
corresponding lag for use in higher-numbered ones may be 
even greater than one. This point will be stronger the more 
stable one believes the dynamic system to be. It arises because 
the effects of serial correlation in sector and equation implicit 
disturbances are direct in the case of lagged endogenous vari- 
ables used in the same or lower-numbered sectors and are 
passed through a damped dynamic system in the case of lagged 
endogenous variables used in higher-numbered sectors (°°). 
To sum up: so far as inconsistency is concerned, it is likely 
to be safer to use endogenous variables with a given lag as 
instruments in higher-numbered sectors than to use them in the 
same or lower-numbered sectors. For the latter use, the endo- 
genous variables should be lagged by at least one more period 
to achieve the same level of consistency (31). 
(°) All this is subject to the minor reservation discussed above concern- 
ing sums each term of which approaches zero monotonically. In practice, 
one tends to ignore such reservations in the absence of specific information 
as to which way they point. 
(*!) The reader should be aware of the parallel between this result and 
the similar result for the use of current endogenous variables which emerges 
when (BR.1)-(BR.3) are assumed. Essentially. we have replaced (BR.2) 
with (5.10) and have dropped (BR.3). 
61 Fisher - pag. 42